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Abstract: The goal of this paper is to apply Laplace transform method to solving the problem of recovery of concentration of tau protein in an axon after a photobleaching experiment that is described in S. Konzack, E. Thies, A. Marx, E. Mandelkow, E. Mandelkow, Swimming against the tide: Mobility of the microtubule-associated protein tau in neurons, Journal of Neuroscience. 27 (2007) 9916-9927. The model accounts for two populations of tau molecules: those that are suspended in the cytoplasm, free to diffuse in the axon, and those that are bound to microtubules (MTs). The exchange of tau molecules between these two populations is modeled by first-order reactions. It is shown that governing equations for this model can be solved by Laplace transform method, although the last step of the solution, finding the inverse Laplace transform, has to be done numerically, which leads to a hybrid analytical and numerical solution technique. The numerical inversion of the Laplace transform is performed utilizing a method based on Fourier series expansion of the inverse transform. [Copyright &y& Elsevier]

Alzheimer's disease (AD) is a neurodegenerative disease that accounts for 70% of all dementia. Early stage diagnosis of AD is essential as there is no certain treatment after the lesion has progressed in the late stage. Nevertheless, there are still limitations of early diagnosis of AD using neuroimaging and psychological memory assessments. Here, we demonstrate ultrasensitive and multiplexed detection of pivotal AD biomarkers (Aβ 1-42 and t-Tau) in biofluids using a reduced graphene oxide field-effect transistor (gFET). The proposed approach provides a wide logarithmically linear range of detection from 10−1–105 pg mL−1 and a femtomolar-level limit of detection in biofluids (human plasma and artificial cerebrospinal fluid) as well as phosphate-buffered saline (PBS). Furthermore, as these core biomarkers have different surface charges in physiological conditions based on the isoelectric point (pI), we achieved a distinctive output signal for each biomarker. The gFET biosensor platform presented in this paper has great potential and can be used for early diagnosis of AD in clinical practice as well as accurate analysis based on the surface charge of the analytes. • The amyloid-β (Aβ) and tau protein in biofluids are pivotal biomarkers for the early stage diagnosis of Alzheimer's disease. • A graphene-based field-effect transistor (gFET) is designed for multiplexed detection of Aβ 1-42 and total tau (t-Tau). • Aβ 1-42 and t-Tau possess different charges owing to their isoelectric point, resulting in distinctive doping effects on gFET. • Femtomolar detection of Aβ 1-42 and total tau (t-Tau) have been achieved in human plasma and artificial cerebrospinal fluid. [ABSTRACT FROM AUTHOR]